Allasia, G.; Besenghi, R. Numerical evaluation of the Kummer function with complex argument by the trapezoidal rule. (English) Zbl 0779.65013 Rend. Semin. Mat., Torino 49, No. 3, 315-327 (1991). The Kummer function \(\Phi(a,c;z)\), expressed in its well-known integral form, is numerically evaluated for complex values of \(z\) by means of the trapezoidal rule. The achieved high degree of accuracy is explained through a detailed investigation of the related Euler-Maclaurin formula. Theoretically interesting error bounds are given. Recurrence relations are used for obtaining \(a\) and \(c\) values for which the trapezoidal rule is not suitable. The procedure is compared with one based on Gauss-Jacobi quadrature. Reviewer: N.M.Temme (Amsterdam) MSC: 65D20 Computation of special functions and constants, construction of tables 33C15 Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\) Keywords:Kummer function; trapezoidal rule; Euler-Maclaurin formula; error bounds; Recurrence relations; Gauss-Jacobi quadrature PDF BibTeX XML Cite \textit{G. Allasia} and \textit{R. Besenghi}, Rend. Semin. Mat., Torino 49, No. 3, 315--327 (1991; Zbl 0779.65013) OpenURL Digital Library of Mathematical Functions: §13.29(iii) Integral Representations ‣ §13.29 Methods of Computation ‣ Computation ‣ Chapter 13 Confluent Hypergeometric Functions